The letter $e$ was selected to represent the irrational number 2.718281828459, in honour of the great Swiss mathematician Leonhard Euler (1706 - 1781).

$e$ is defined as the limit of $(1 + 1/n)^n$ as n approaches ∞.

It may also be expressed as:

$$e = ∑↙{n=0}↖{∞} 1/{n!} = 1 + 1/1 + 1/{1⋅2} + 1/{1⋅2⋅3} + ...$$

Derivatives of Trigonometric Functions

Observing the graph of sine of $x$, it can be seen that the slope is graphed by cosine $x$. When $x$ is zero, sine is zero, with increasing tangent gradient. At zero, the slope is maximum, and gradually decreases, but not constantly, to where it levels out at $π/2$, where the tangent gradient is zero.

cosine is therefore the first derivative of the sine function.

Since the sine and cosine graphs superimpose if sine is translated $π/2$ to the left, cos$x = $sin$(x+π/2)$.